Method of manufacturing a contact lens

ABSTRACT

The present invention provides a method for converting a desired lens design to a geometry of a contact lens, preferably a customized contact lens or a contact lens having a complex surface design, to be produced in a computer-controlled manufacturing system. The method comprises: providing a lens design of a contact lens having a central axis, an anterior surface and an opposite posterior surface; projecting a predetermined number of points within a predetermined surface tolerance onto a surface of the lens design along each of a desired number of evenly-spaced semi-diameter spokes, each spoke radiating outwardly from the central axis; and for each of the spokes, generating a semi-meridian which is continuous in first derivative and includes a series of arcs and optionally straight lines, wherein each arc is defined by fitting at least three consecutive points into a spherical mathematical function within a desired concentricity tolerance, wherein each of the straight lines is obtained by connecting at least three consecutive points.

This application is a national stage filing under 35 U.S.C. 371 ofInternational Application No. PCT/EP03/08084 filed Jul. 23, 2003, whichclaims benefits of U.S. Provisional Patent Application No. 60/398,495filed Jul. 24, 2002.

The present invention relates to a method for designing and/or producinga contact lens, preferably a customized contact lens or a contact lenshaving a complex surface design. In particular, the present invention isrelated to a method for converting a desired lens design to a geometryof a contact lens to be produced in a manufacturing system.

Contact lenses are widely used for correcting many different types ofvision deficiencies. Current contact lenses have relatively simplesurface design, generally are rotationally-symmetric or toric, and canonly correct low-order aberrations of the human eye, such as defocus,astigmatism and prism. Current contact lenses are unable to correcthigh-order monochromatic aberrations of the human eye, such as anon-standard amount of spherical aberration, coma, and other irregularhigh-order aberrations. These high order aberrations blur images formedon the retina, which can impair vision. The impact of these higher-orderaberrations on retinal image quality can become significant in somecases, for example, in older eyes, in normal eyes with large pupils, andin the eyes of many people with irregular astigmatism, keratoconus,corneal dystrophies, post penetrating keratoplasty, scarring fromulcerative keratitis, corneal trauma with and without surgical repair,and sub-optimal outcome following refractive surgery. For those people,visual acuity of 20/20 or better can be achieved with customized contactlenses or contact lenses capable of correcting high-order monochromaticaberrations of the human eye. Unlike current contact lenses, customizedcontact lenses or contact lenses capable of correcting high orderaberrations inevitably need to have a complex surface design withoutrestrictions of rotational symmetry.

Advances in computer aided design (CAD) technologies may permit todesign a customized contact lens, for example, using polynomials and/orspline-based mathematical functions, and then to constructmathematically high order surfaces, such as NURBS (Non-Uniform RationalB-splines) or Beizier surfaces, of an intended design. Themathematically high order surfaces of the intended design then needs tobe converted into control signals, which control a computer controllablemanufacturing device (for example, lathes, grinding and millingmachines, molding equipments, or lasers) to produce directly acustomized contact lens or molding tools for producing a customizedcontact lens. However, few currently-known processes could convertmathematically high order surfaces of a lens design into control signalsor at least in an automatic manner. Therefore, there is a need for amethod capable of automatically converting mathematically high ordersurfaces of a lens design into control signals, which control a computercontrollable manufacturing device to produce a customized contact lens.

An object of the invention is to provide a method for convertingmathematically high order surfaces of a lens design into controlsignals, which control a computer controllable manufacturing device toproduce a customized contact lens.

Another object of the invention is to provide a method for producing acustomized contact lens having a complex surface design withoutrestrictions of rotational symmetry.

SUMMARY OF THE INVENTION

In accomplishing the foregoing, there is provided, in accordance withone aspect of the present invention, a method for converting a desiredlens design to a geometry of an ophthalmic lens to be produced in amanufacturing system. The ophthalmic lens can be any contact lens,preferably a customized contact lens or a contact lens having a complexsurface design. The method comprises: providing a lens design of acontact lens having a central axis, an anterior surface and an oppositeposterior surface; projecting a predetermined number of points within apredetermined surface tolerance onto a surface of the lens design alongeach of a desired number of evenly-spaced semi-diameter spokes, eachspoke radiating outwardly from the central axis; and for each of thespokes, generating a semi-meridian which is continuous in firstderivative and includes a series of arcs and optionally straight lines,wherein each arc is defined by fitting at least three consecutive pointsinto a spherical mathematical function within a desired concentricitytolerance, wherein each of the straight lines is obtained by connectingat least three consecutive points.

The invention, in another aspect, provides a method for producing anophthalmic lens, preferably a customized contact lens or a contact lenshaving a complex surface design. The method comprises: providing a lensdesign of a contact lens having a central axis, an anterior surface andan opposite posterior surface; projecting a predetermined number ofpoints within a predetermined tolerance onto a surface of the lensdesign along each of a desired number of evenly-spaced semi-diameterspokes, each spoke radiating outwardly from the central axis; for eachof the spokes, generating a semi-meridian which is continuous in firstderivative and includes a series of arcs and optionally straight lines,wherein each arc is defined by fitting at least three consecutive pointsinto a spherical mathematical function, wherein each of the straightlines is obtained by connecting at least three consecutive points;generating a data file containing information about the geometry of thelens in a form that is interpretable by a computer-controlledmanufacturing device; and producing the contact lens or a molding toolfor making the contact lens using the computer-controlled manufacturingdevice.

These and other aspects of the invention will become apparent from thefollowing description of the preferred embodiments taken in conjunctionwith the following drawings. As would be obvious to one skilled in theart, many variations and modifications of the invention may be effectedwithout departing from the spirit and scope of the novel concepts of thedisclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically shows the design of a translating contact lenshaving an optical zone, a ramped ridge zone below the optical zone, anda ridge-off zone above the optical zone on the anterior surface of thetranslating contact lens.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Reference now will be made in detail to the embodiments of theinvention. It will be apparent to those skilled in the art that variousmodifications and variations can be made in the present inventionwithout departing from the scope or spirit of the invention. Forinstance, features illustrated or described as part of one embodiment,can be used on another embodiment to yield a still further embodiment.Thus, it is intended that the present invention cover such modificationsand variations as come within the scope of the appended claims and theirequivalents. Other objects, features and aspects of the presentinvention are disclosed in or are obvious from the following detaileddescription. It is to be understood by one of ordinary skill in the artthat the present discussion is a description of exemplary embodimentsonly, and is not intended as limiting the broader aspects of the presentinvention.

Unless defined otherwise, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. Generally, the nomenclatureused herein and the laboratory procedures are well known and commonlyemployed in the art. Conventional methods are used for these procedures,such as those provided in the art and various general references. Wherea term is provided in the singular, the inventors also contemplate theplural of that term. The nomenclature used herein and the laboratoryprocedures described below are those well known and commonly employed inthe art.

In one embodiment, the present invention provides a method forconverting a desired lens design to a geometry of a contact lens to beproduced in a manufacturing system. The method of the inventioncomprises: providing a lens design of a contact lens having a centralaxis, an anterior surface and an opposite posterior surface; projectinga predetermined number of points within a predetermined surfacetolerance onto a surface of the lens design along each of a number ofevenly-spaced semi-diameter spokes, each spoke radiating outwardly fromthe central axis; and for each of the spokes, generating a semi-meridianwhich is continuous in first derivative and includes a series of arcsand optionally straight lines, wherein each arc is defined by fitting atleast three consecutive points into a spherical mathematical functionwithin a desired concentricity tolerance, wherein each of the straightlines is obtained by connecting at least three consecutive points.

It is well known to those skilled in the art that a lens design for acontact lens can be carried out by using an optical computer aideddesign (CAD) system and a mechanical CAD system.

An optical CAD system is used to design an optical model lens. “Anoptical model lens” refers to an ophthalmic lens that is designed in acomputer system and generally does not contain other non-optical systemswhich are parts of an ophthalmic lens. Exemplary non-optical systems ofa contact lens include, but are not limited to bevel, lenticular, andedge that joins the anterior and posterior surfaces of a contact lens.

“A bevel” refers to a non-optical surface zone located at the edge ofthe posterior surface of a contact lens. Generally, the bevel is asignificantly flatter curve and is usually blended with the base curve(optical posterior surface) of a contact lens and appears as an upwardtaper near the edge. This keeps the steeper base curve radius fromgripping the eye and allows the edge to lift slightly. This edge lift isimportant for the proper flow of tears across the cornea and makes thelens fit more comfortably.

“A lenticular” refers to a non-optical surface zone of the anteriorsurface of a contact lens between the optical zone and the edge. Theprimary function of the lenticular is to control the thickness of thelens edge.

Any known, suitable optical computer aided design (CAD) system may beused to design an optical model lens. Exemplary optical computer aideddesign systems includes, but are not limited to Advanced System Analysisprogram (ASAP) from Breault Research Organization and ZEMAX (FocusSoftware, Inc.). Preferably, the optical design will be performed usingAdvanced System Analysis program (ASAP) from Breault ResearchOrganization with input from ZEMAX (Focus Software, Inc.).

The design of the optical model lens can be transformed by, for example,a mechanical CAD system, into a set of mechanical lens design thatincludes optical zones, non-optical zones and non-optical features.Exemplary non-optical zones and features of a contact lens include, butare not limited to bevel, lenticular, edge that joins the anterior andposterior surfaces of a contact lens, orientation features, and thelike. Exemplary orientation features include, but are not limited to, aprism ballast or the like that uses a varying thickness profile tocontrol the lens orientation, a faceted surface (e.g., ridge-off zone)in which parts of the lens geometry is removed to control the lensorientation, a ridge feature which orients the lens by interacting withthe eyelid. Preferably, when transforming the design of an optimizedoptical model lens into a mechanical lens design, some common featuresof a family of contact lenses can be incorporated.

Any know, suitable mechanical CAD system can be used in the invention.Preferably, a mechanical CAD system capable of representing preciselyand mathematically high order surfaces is used to design a contact lens.An example of such mechanical CAD system is Pro/Engineer.

Preferably, the design of a contact lens may be translated back andforth between the optical CAD and mechanical CAD systems using atranslation format which allows a receiving system, either optical CADor mechanical CAD, to construct NURBs or Beizier surfaces of an intendeddesign. Exemplary translation formats include, but are not limited to,VDA (verband der automobilindustrie) and IGES (Initial Graphics ExchangeSpecification). By using such translation formats, overall surface oflenses can be in a continuous form that facilitates the production oflenses having radially asymmetrical shapes. Beizier and NURBs surfaceare particular advantageous for presbyopic design because multiple zonescan be blended, analyzed and optimized.

After the optical and mechanical design for a contact lens is completed,a lens design is typically in a neutral file format, for example, suchas IGES or VDA, or in a proprietary file format (for example, a Pro/Efile format). A predetermined number of points are projected within apredetermined surface tolerance onto a surface of the lens design alongeach of a desired number of evenly-spaced semi-diameter spokes.

A “surface tolerance” refers to the position deviation of a projectedpoint from an ideal position on a surface of a lens design. Thedeviation can be in the direction either parallel or perpendicular tothe central axis of a lens design.

A “spoke” refers to a ray radiating outwardly from the central axis andis perpendicular to the central axis. A “semi-diameter spoke” refers toa line segment from the central axis to the edge of a lens design.

“Evenly-spaced semi-diameter spokes” means that all semi-diameter spokesradiate outwardly from the central axis and separate from each other byone equal angle. The number of evenly-spaced semi-diameter spokes can beany number, depending on the complex features of a surface of a lensdesign and/or on the specification of a computer controllable lathe.Preferably, a numerically controlled lathe from Precitech, Inc., forexample, such as Optoform ultra-precision lathes (models 30, 40, 50 and80) having Variform piezo-ceramic fast tool servo attachment, is used inthe invention. For Optoform ultra-precision lathes (models 30, 40, 50and 80) having Variform piezo-ceramic fast tool servo attachment, thenumber of semi-meridians can be 1, 24, 96 or 384, preferably is 24 or96.

Points can be projected onto a surface of the lens design along asemi-diameter spoke in a direction parallel to the central axis or in adirection normal to the surface. The number of points to be projectedcan be determined in a various ways.

In a first example, the number of points to be projected along onesemi-diameter spoke can be determined by dividing the distance from thecentral axis to lens edge by a point spacing of at least 1 micron,preferably from about 5 to about 25 microns, more preferably from about5 to about 15 microns, even more preferably about 10 microns. A “pointspacing” refers to a distance between two points along the semi-diameterspoke.

In a second example, the number of points to be projected along onesemi-diameter spoke can be determined as follows. First, evenly-spacedpoints are projected along a semi-diameter probing spoke at an azimuthalangle at which complicated features of the surface are located. Eachpairs of points are separating by a point spacing of 5 to 25 microns.Then, all of the projected points are divided into a series of groups,each group composed of three consecutive points, a first point, a middlepoint and a third point. Each of the points can belong to either onegroup or two groups. For example, in a directional order from thecentral axis to the edge, group j is composed of point i, point i+1, andpoint i+2; group j+1 is composed of point i+1, point i+2, and point i+3.One group at a time from the central axis to the edge or from the edgeto the central axis, the curvature of the surface at the middle point ofthe group is analyzed by comparing a distance between the middle pointi+1 and a line linking the first point i and the third point i+2 of thecorresponding group with the predetermined surface tolerance. If thedistance between the middle point and the line linking the first andthird points oft the group is larger than the predetermined surfacetolerance, the curvature of the surface at that point is sharp and anadditional point needs to be projected between the first and the middlepoints in that group. The point spacing between the first and theadditional points is equal to point spacing between the additional andmiddle points. After adding an additional point, all of the pointsincluded the newly added point is regrouped again and the curvature ofthe surface at the middle point of each of the series of groups isanalyzed. Such iterative procedure is repeated until the distancebetween the middle point of each of the series of groups and the linelinking the first and the third points of corresponding group along theprobing spoke is less than or equal to the predetermined surfacetolerance. In this way, the number of the points to be projected ontothe surface of the lens design along each of the desired number ofevenly-spaced semi-diameter spokes and point spacings for a series ofpairs of neighboring points can be determined.

In a preferred embodiment, after the number of points are predeterminedaccording to the procedure described in the first example describedabove and then projected onto a surface of the lens design along each ofa number of evenly-spaced semi-diameter spokes, the curvature of thesurface at each of the projected points alone each of semi-diameterspokes is checked to see if it changes sharply. Where the curvature ofthe surface at a projected point changes sharply, additional points mayneed to be projected to faithfully represent the lens design. All of thepoints along each of semi-diameter spokes are grouped into a series ofgroups, each group composed of three consecutive points, a first point,a middle point and a third point. Each of the points can belong toeither one group or two groups. One group at a time from the centralaxis to the edge or from the edge to the central axis, the curvature ofthe surface at the middle point of the group is analyzed by comparing adistance between the middle point and a line linking the first point andthe third point of the corresponding group with the predeterminedsurface tolerance. If the distance between the middle point and the linelinking the first and third points of the group is larger than thepredetermined surface tolerance, an additional point is projectedbetween the first and the middle points in that group, wherein pointspacing between the first and additional points is equal to pointspacing between the additional and middle points. After adding anadditional point, all of the points included the newly added point isregrouped again and the curvature of the surface at the middle point ofeach of the series of groups is analyzed. Such iterative procedure is,repeated until the distance between the middle point of each of theseries of groups and the line linking the first and the third points ofcorresponding group along the probing spoke is within the predeterminedsurface tolerance. In this way, any complex features of a surface of thelens design can be reproduced.

For each of the semi-diameter spokes, a semi-meridian which iscontinuous in first derivative is generated. The semi-meridian includesa series of arcs and optionally straight lines, wherein each arc isdefined by fitting at least three consecutive points into a sphericalmathematical function within a desired concentricity tolerance. A“concentricity tolerance” refers to the allowed deviation of a pointfrom a given arc. Each of the straight lines is obtained by connectingat least three consecutive points. Preferably, arc fitting routine isstarted from the central axis to the edge.

After converting a desired lens design to a geometry of a contact lensto be produced in a manufacturing system, a data file is generated tocontain information about the geometry of the lens in a form that isinterpretable by a computer-controlled manufacturing device.

In another embodiment, the present invention provides a method forproducing an ophthalmic lens, preferably a customized contact lens or acontact lens having a complex surface design. The production methodcomprises: providing a lens design of a contact lens having a centralaxis, an anterior surface and an opposite posterior surface; projectinga predetermined number of points within a predetermined tolerance onto asurface of the lens design along each of a number of evenly-spacedsemi-diameter spokes, each spoke radiating outwardly from the centralaxis; for each of the spokes, generating a semi-meridian which iscontinuous in first derivative and includes a series of arcs andoptionally straight lines, wherein each arc is defined by fitting atleast three consecutive points into a spherical mathematical function,wherein each of the straight lines is obtained by connecting at leastthree consecutive points; generating a data file containing informationabout the geometry of the lens in a form that is interpretable by acomputer-controlled manufacturing device; and producing the contact lensor a molding tool for making the contact lens using thecomputer-controlled manufacturing device.

A computer controllable manufacturing device is a device that can becontrolled by a computer system and that is capable of producingdirectly an ophthalmic lens or an optical tools for producing anophthalmic lens. Any known, suitable computer controllable manufacturingdevice can be used in the invention. Preferably, a computer controllablemanufacturing device is a numerically controlled lathe, preferably atwo-axis lathe with a 45° piezo cutter or a lathe apparatus disclosed byDurazo and Morgan in U.S. Pat. No. 6,122,999, herein incorporated byreference in its entirety, more preferably a numerically controlledlathe from Precitech, Inc., for example, such as Optoformultra-precision lathes (models 30, 40, 50 and 80) having Variformpiezo-ceramic fast tool servo attachment.

A data file containing information about the geometry of the lens in aform that is interpretable by a computer-controlled manufacturing devicecan be generated to conform with the specification of a numericallycontrolled lathe. For example, a zero semi-meridian is required to begenerated before the Variform can perform a non-symmetric cutting pass.The zero semi-meridian is based on the average height of each of theother meridians at each radial location. The zero semi-meridian givesthe Variform a zero position on which it can base its oscillationcalculations. Then, a mini-file is created which includes both theinformation for the header and the geometry of the lens in a form thatcan be interpreted by the lathe. Each of semi-meridians has a number ofzones or arcs. Since all semi-meridians must have the same number ofzones, zero diameter arcs can be created or last zone is copy for anumber of time to equalize the numbers of zones for all meridians. Afterthe file is complete, it can be loaded into the lathe and run to producea contact lens.

The methods of the present invention can be used in manufacturing acontact lens having a complex surface design, for example, the complexdesign of a translating contact lens, shown in FIG. 1. The translatingcontact lens 100 has a top 108, a bottom 109, a central axis 102, aposterior surface 104 and an opposite anterior surface 106. The anteriorsurface 106 includes an optical zone 110, a transition zone 140, aramped ridge zone 150, a ridge-off zone 160 and a lenticular zone 170.

The transition zone 140 provides a smooth transition from the rampedridge zone 150 to the optical zone 110. The transition zone 140 extendsfrom the lower edge 114 of the optical zone 110 to the upper edge of theramped ridge zone 156.

The ramped ridge zone 150 provides vertical translation support for thelens 100. The ramped ridge zone 150 is disposed below the optical zone110. The ramped ridge zone 150 has an upperedge, a lower ramped edge, alatitudinal ridge extends outwardly from the anterior surface 106, and aramp that extends downwardly from the lower ramped edge. When the eyemoves in a downward direction, the ramp, the lower ramp edge and thelatitudinal ridge can engage with the user's lower eyelid, and supportsthe lens 100, thereby allowing translation of the lens 100 across thesurface of the eye. The elevation height of the latitudinal ridge arehigher at the both ends than in the middle and two bumps (152, 153) areformed at the two ends. The latitudinal ridge has a mirror symmetry withrespect to a plan, which cuts the latitudinal ridge in the middle intotwo equal part and contains the central axis. Such latitudinal ridge canimprove wearer's comfort, since translating stress may be uniformlydistributed over the entire lens-interacting portion of the lowereyellid. Such a preferred feature of a ramped ridge zone can be achievedby using a continuous surface defined by a conic or spline-basedmathematical function or made of several different surface patches.

The transition from the lenticular zone to the ramped ridge zone iscontinuous in first derivative (tangent to each other), preferablycontinuous in second derivative. The ramp has a cuvature or slope thatprovides a varying degree of interaction between the ramped ridge zoneand the lower eyelid depending on where the lower eyelid stricks theramped ridge zone. With such ramp, the lower eyelid of the eye isengaged with at least some portion of the ramped ridge zone at all timesand thereby effect the lens position on the eye in primary gaze(horizontal gaze) and/or lens translating amount across the surface ofan eye when the eye changes from the horizontal (primary) gaze (distantvision) to a down gaze (intermediate or near vision).

One advantage of incorporating a ramp in the ramped ridge zone is thatit can provide a smooth transition zone for the eyelid to “ramp up” theridge. This gradual engagement will benefit the wearer by increasingcomfort and reducing lens sensation in the eye because the ridge willalways be engaged.

Another advantage of incorporating a ramp in the ramped ridge zone isthat, since the ramp slope can determine lens position on an eye inprimary gaze (horizontal), a lens design for a desired visualperformance can be reliably implemented in the production of translatingcontact lenses.

Conversion of the lens design shown in FIG. 1 is carried out as follows.First, an user defines a set of parameters, such as a surface tolerance,a concentricity tolerance, orientation of the lens design, the number ofspokes to be generated for each of the anterior and posterior surfaces,creating zero point at 0,0, orientation of Z-axis, and type of lenssurface (concave or convex surface) to be converted into a geometry.Then, the number of points to be projected onto the a surface of thelens design (for example, the anterior surface) along each of the numberof evenly-spaced semi-diameter spokes in a direction parallel to thecentral axis. A semi-diameter spoke 210 at an azimuthal angle at whichone of the two bumps of the anterior surface is located is selected asthe semi-diameter probing spoke. Evenly-spaced points are projectedalong the semi-diameter probing spoke, wherein each pairs of points areseparating by a point spacing of 10 microns.

Then, all of the projected points are divided into a series of groups,each group composed of three consecutive points, a first point, a middlepoint and a third point. Each of the points can belong to either onegroup or two groups. One group at a time from the central axis to theedge or from the edge to the central axis, the curvature of the surfaceat the middle point of the group is analyzed by comparing a distancebetween the middle point and a line linking the first point and thethird point of the corresponding group with the predetermined surfacetolerance. If the distance between the middle point and the line linkingthe first and third points of the group is larger than the predeterminedsurface tolerance, an additional point is projected between the firstand the middle points in that group, wherein point spacing between thefirst and additional points is equal to point spacing between theadditional and middle points. After adding an additional point, all ofthe points included the newly added point is regrouped again and thecurvature of the surface at the middle point of each of the series ofgroups is analyzed. Such iterative procedure is repeated until thedistance between the middle point of each of the series of groups andthe line linking the first and the third points of corresponding groupalong the probing spoke is equal to or less than the predeterminedsurface tolerance. In this way, the number of the points to be projectedonto the surface of the lens design along each of the desired number ofevenly-spaced semi-diameter spokes and point spacings for a series ofpairs of neighboring points are determined.

The above-determined number of points are projected onto the anteriorsurface of the lens design shown in FIG. 1 along each of 96semi-diameter spokes. For each of the 96 semi-diameter spokes, asemi-meridian which is continuous in first derivative is generated. Thesemi-meridian includes a series of arcs and optionally straight lines,wherein each arc is defined by fitting at least three consecutive pointsinto a spherical mathematical function within a desired concentricitytolerance. Each of the straight lines is obtained by connecting at leastthree consecutive points. Preferably, arc fitting routine is startedfrom the central axis to the edge.

Similarly, conversion of the posterior surface of the lens design shownin FIG. 1 into a geometry can be carried out according to the abovedescribed procedure.

After converting the lens design shown in FIG. 1 to a geometry of acontact lens to be produced in a manufacturing system, a mini-filecontaining both the information for the header and the information aboutthe geometry of the lens is generated. This mini-file also contains azero semi-meridian that is based off the average height of each of theother meridians at each radial location and that gives the Variform azero position on which it can base its oscillation calculations. In thismini-file, all semi-meridians have the same number of zones. This isaccomplished by copying the last zone of a semi-meridian for a number oftime to equalize the numbers of zones for all meridians. After themini-file is complete, it is loaded into an Optoform ultra-precisionlathe (models 30, 40, 50 or 80) having Variform piezo-ceramic fast toolservo attachment and run to produce a translating contact lens.

The invention has been described in detail, with particular reference tocertain preferred embodiments, in order to enable the reader to practicethe invention without undue experimentation. A person having ordinaryskill in the art will readily recognize that many of the previouscomponents, compositions, and/or parameters may be varied or modified toa reasonable extent without departing from the scope and spirit of theinvention. Furthermore, titles, headings, example materials or the likeare provided to enhance the reader's comprehension of this document, andshould not be read as limiting the scope of the present invention.Accordingly, the invention is defined by the following claims, andreasonable extensions and equivalents thereof.

1. A method for converting a desired lens design to a geometry of acontact lens to be produced in a manufacturing system, the methodcomprises: (1) providing a lens design of a contact lens having acentral axis, an anterior surface and an opposite posterior surface; (2)projecting a predetermined number of points within a predeterminedsurface tolerance onto a surface of the lens design along each of anumber of evenly-spaced semi-diameter spokes, each spoke radiatingoutwardly from the central axis; (3) for each of the spokes, generatinga semi-meridian which is continuous in first derivative and includes aseries of arcs and optionally straight lines, wherein each arc isdefined by fitting at least three consecutive points into a sphericalmathematical function within a specified concentricity tolerance,wherein each of the straight lines is obtained by connecting at leastthree consecutive points; and (4) generating a data file containinginformation about the geometry of the lens in a form that isinterpretable by a computer-controlled manufacturing device.
 2. A methodof claim 1, wherein the number of the points to be projected onto thesurface of the lens design along each of the semi-diameter spokes isdetermined by dividing the distance from the central axis to lens edgeby a point spacing of at least about 1 micron.
 3. A method of claim 2,wherein the point spacing is from about 5 to about 25 microns.
 4. Amethod of claim 3, further comprising projecting additional points in aregion where the curvatures of the surface change sharply.
 5. A methodof claim 4, wherein the step of projecting additional points isperformed according to a procedure including: (i) grouping all of thepoints projected along a semi-diameter spoke into a series of groups,each group composed of three consecutive points, a first point, a middlepoint and a third point; (ii) one group at a time from the central axisto the edge or from the edge to the central axis, analyzing thecurvature of the surface at the middle point of the group by comparing adistance between the middle point and a line linking the first and thethird points of the corresponding group with the predetermined surfacetolerance; (iii) projecting an additional point between the first andthe middle points in the group, provided that the distance between themiddle point and the line linking the first and third points of thegroup is larger than the predetermined surface tolerance; and (iv)repeating steps (i) to (iii) until the distance between the middle pointof each of the series of groups of points projected along thesemi-diameter spoke and the line linking the first and the third pointsof corresponding group is equal to or less than the predeterminedsurface tolerance.
 6. A method of claim 5, wherein the number of theevenly-spaced semi-diameter spokes is a number between 24 to
 384. 7. Amethod of claim 6, wherein the contact lens is a customized contact lensor a contact lens having a complex surface design.
 8. A method of claim1, wherein the number of the points to be projected onto the surface ofthe lens design along each of the number of evenly-spaced semi-diameterspokes is determined according to a procedure including: (I) projectingevenly-spaced points separating by a point spacing of about 5 to about25 microns along a semi-diameter probing spoke at an azimuthal angle atwhich one or more complicated features of the surface are located; (II)dividing all of the points into a series of groups, each group composedof three consecutive points, a first point, a middle point and a thirdpoint; (III) one group at a time from the central axis to the edge orfrom the edge to the central axis, analyzing the curvature of thesurface at the middle point of the group by comparing a distance betweenthe middle point and a line linking the first and the third points ofthe corresponding group with the predetermined surface tolerance; (IV)projecting an additional point between the first and the middle pointsin the group, provided that the distance between the middle point andthe line linking the first and third points of the group is larger thanthe predetermined surface tolerance, wherein point spacing between thefirst and additional points is equal to point spacing between theadditional and middle points; (V) repeating steps (II) to (IV) until thedistance between the middle point of each of the series of groups andthe line linking the first and the third points of corresponding groupalong the probing spoke is equal to or less than the predeterminedtolerance; and (VI) outputting the number of the points to be projectedonto the surface of the lens design along each of the number ofevenly-spaced semi-diameter spokes and point spacings for pairs ofneighboring points.
 9. A method of claim 8, wherein the number of theevenly-spaced semi-diameter spokes is a number between 24 to
 384. 10. Amethod of claim 9, wherein the contact lens is a customized contact lensor a contact lens having a complex surface design.
 11. A method forproducing a contact lens, comprises: (1) providing a lens design of acontact lens having a central axis, an anterior surface and an oppositeposterior surface; (2) projecting a predetermined number of pointswithin a predetermined tolerance onto a surface of the lens design alongeach of a number of evenly-spaced semi-diameter spokes, each spokeradiating outwardly from the central axis; (3) for each of the spokes,generating a semi-meridian which is continuous in first derivative andincludes a series of arcs and optionally straight lines, wherein eacharc is defined by fitting at least three consecutive points into aspherical mathematical function, wherein each of the straight lines isobtained by connecting at least three consecutive points; (4) generatinga data file containing information about the geometry of the lens in aform that is interpretable by a computer-controlled manufacturingdevice; and (5) producing the contact lens or a molding tool for makingthe contact lens using the computer-controlled manufacturing device. 12.A method of claim 11, wherein the number of the points to be projectedonto the surface of the lens design along each of the semi-diameterspokes is determined by dividing the distance from the central axis tolens edge by a point spacing of at least about 1 micron.
 13. A method ofclaim 12, wherein the point spacing is from about 5 to about 25 microns.14. A method of claim 13, further comprising projecting additionalpoints in a region where the curvatures of the surface change sharply.15. A method of claim 14, wherein the step of projecting additionalpoints is performed according to a procedure including: (i) grouping allof the points projected along a semi-diameter spoke into a series ofgroups, each group composed of three consecutive points, a first point,a middle point and a third point; (ii) one group at a time from thecentral axis to the edge or from the edge to the central axis, analyzingthe curvature of the surface at the middle point of the group bycomparing a distance between the middle point and a line linking thefirst and the third points of the corresponding group with thepredetermined surface tolerance; (iii) projecting an additional pointbetween the first and the middle points in the group, provided that thedistance between the middle point and the line linking the first andthird points of the group is larger than the predetermined surfacetolerance; and (iv) repeating steps (i) to (iii) until the distancebetween the middle point of each of the series of groups of pointsprojected along the semi-diameter spoke and the line linking the firstand the third points of corresponding group is equal to or less than thepredetermined surface tolerance.
 16. A method of claim 15, wherein thenumber of the evenly-spaced semi-diameter spokes is a number between 24to
 384. 17. A method of claim 16, wherein the contact lens is acustomized contact lens or a contact lens having a complex surfacedesign.
 18. A method of claim 11, wherein the number of the points to beprojected onto the surface of the lens design along each of the numberof evenly-spaced semi-diameter spokes is determined according to aprocedure including: (I) projecting evenly-spaced points separating by apoint spacing of about 5 to about 25 microns along a semi-diameterprobing spoke at an azimuthal angle at which one or more complicatedfeatures of the surface are located; (II) dividing all of the pointsinto a series of groups, each group composed of three consecutivepoints, a first point, a middle point and a third point; (III) one groupat a time from the central axis to the edge or from the edge to thecentral axis, analyzing the curvature of the surface at the middle pointof the group by comparing a distance between the middle point and a linelinking the first and the third points of the corresponding group withthe predetermined surface tolerance; (IV) projecting an additional pointbetween the first and the middle points in the group, provided that thedistance between the middle point and the line linking the first andthird points of the group is larger than the predetermined surfacetolerance, wherein point spacing between the first and additional pointsis equal to point spacing between the additional and middle points; (V)repeating steps (ii) to (iv) until the distance between the middle pointof each of the series of groups and the line linking the first and thethird points of corresponding group along the probing spoke is equal toor less than the predetermined tolerance; and (VI) outputting the numberof the points to be projected onto the surface of the lens design alongeach of the number of evenly-spaced semi-diameter spokes and pointspacings for pairs of neighboring points.
 19. A method of claim 18,wherein the number of the evenly-spaced semi-diameter spokes is a numberbetween 24 to
 384. 20. A method of claim 19, wherein the contact lens isa customized contact lens or a contact lens having a complex surfacedesign.